Find the area of each regular polygon with the given apothem a and side length s. decagon, a = 19 m, s = 12.3 m

A homeowner buys a new refrigerator and a new air conditioner. Which one of these devices would you expect to have a higher COP? Why?

For a sample of eight apartment buildings in Chicago, the percentage-occupancy rates during a recent month were as shown below:

$$\begin{array}{llll}50.0 \% & 79.1 & 61.3 & 43.9 \\ 68.1 & 70.0 & 72.5 & 66.3\end{array}$$

For these sample data, determine:

c. The standard deviation and variance.

Assume a normal distribution with known population variance. Calculate the LCL and UCL for each of the following.

a. $\bar{x}=50 ; n=64 ; \sigma=40 ; \alpha=0.05$

b. $\bar{x}=85 ; n=225 ; \sigma^2=400 ; \alpha=0.01$

c. $\bar{x}=510 ; n=485 ; \sigma=50 ; \alpha=0.10$

For the equation, solve for $y$ and identify the new coefficient of $x$ and new constant term.

$\frac{5}{6} x+\frac{1}{7} y=-\frac{4}{7}$

The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides. 18

Refer to Appendix page discussed before, to find data about the average number of days with precipitation of $0.01$ in. or more for selected cities in the United States. Using a calculator or computer, enter the data for the annual number of days with precipitation.

Find the mean, range, standard deviation, and variance for this data.

The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides. 72

Let G be an r-regular graph with n vertices and m edges. Find (and prove) a simple algebraic relation between r, n, and m.

Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. $x^{2}+4 x y+y^{2}-3=0$

Solve. The length of a side of the base of a regular square pyramid is 6 in. and the height of the pyramid is 10 in. Find the volume of the pyramid.

Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the variance and standard deviation of the speeds, and interpret the results.

Lo-bed Company produced 4,000 units of product that required four standard hours per unit. The standard fixed overhead cost per units is $1.20 per hour at 16,400 hours, which is 100% of normal capacity. Determine the fixed factory overhead volume variance.

(a) Explain how to find the nth state matrix of a Markov chain. (b) Explain how to find the steady state matrix of a Markov chain. (c) What is a regular Markov chain? (d) What is an absorbing Markov chain? (e) How is an absorb ing Markov chain different than a regular Markov chain?